Let f: R → R be given by f(x) = |x2 - 1|, then
1
f has a local minima at x = ± 1 but no local maxima
2
f has a local maxima at x = 0, but no local minima.
3
f has a local minima at x = ± 1 and a local maxima at x = 0
4
f has neither any local maxima nor any local minima